example 3.3

For Coaxial TE11, to avoid solving

 

 

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the product kc*a can be approximated as function of b/a ratio with the simple expression kc_a(b_over_a)=2/(1+b_over_a)

 

b_over_a=[1:.01:12];

kca_approx=2./(1+b_over_a);

plot(b_over_a,kca_approx);grid on;

ax=gca;axis(ax,[1 12 0 1])

xlabel('b/a');ylabel('kc*a')

legend('approximated kc*a')

 

this graph on right hand side is not the one [POZAR] uses on page 133.

 

da_in=.0645;db_in=.205; % Diameters, both in inches

a_in=da_in/2                   % radii

b_in=db_in/2

in2m=25.40001*1e-3

a=a_in*in2m

b=b_in*in2m

 

One annot plug arbitrary value in vector expecting to match value

kca1_approx=kca_approx(b_in/a_in) returns no integer index error.

 

f_kca_approx=@(x) 2/(1+x);

 

kca1_approx=f_kca_approx(b_in/a_in)

 

f2=@(x) 2/(1+x)-f_kca_approx(b_in/a_in)

bva_approx=fsolve(f2,1)

 

wavenumber of the TE11 cutoff frequency, units: m^-1

 

kc1=kca1_approx/a 

 

c0=299792486;

er=2.2;

fc_TE11=c0*kc1/(2*pi*er^.5)

 

Manufacturers recommend not working right on the edges of bands

f_max_TEM=.95*fc_TE11

 

 

Although kc~2/(a+b) seems to be a commonly used approximation to obtain coaxial TE11 cut-off frequency, it's widely spread in literature, the equation to get all coaxial cut-off frequencies is in [POZAR] page 132.

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